探討Smart 3D-UG APP輔助在真實情境中學習體積與表面積

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鄭芸昀(Yun-Yun Cheng) 查詢紙本館藏

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網路學習科技研究所

論文名稱

探討Smart 3D-UG APP輔助在真實情境中學習體積與表面積
(A Study of Smart 3D-UG APP for Facilitating Learning Volume and Surface Area in Authentic Contexts)

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摘要(中)

隨著智慧型手機設備的普及和使用，透過一支手機便可以隨時隨地的進行學習，特別是透過科技來輔助教學，已是現今教育現場積極推行的教學目標，將科技與周圍的真實生活環境與學習主題聯繫起來，以幫助學生在真實情境中學習，而非將學習侷限在課本當中。因此，如何設計使用智慧型手機的輔助學習課程，變得更具前瞻性，回應在我們的日常生活中與幾何相關的場景，因此開發了一款幾何學習的手機應用程式。
本研究是在真實情境中使用一個名為Smart 3D-UG的數學幾何學習系統來幫助小學生學習體積及表面積。Smart 3D-UG運用了AR擴增實境的技術及智慧回饋，使學生可以針對身邊真實的3D物體進行實際的測量，例如:正方體、長方體、三角柱。此系統還內建多媒體白板，讓學生能直接在白板上計算。
本研究將四十七名六年級小學生分為實驗組及對照組。實驗組使用Smart 3D-UG進行學習，而對照組則使用沒有Smart相關機制，以3D-UG系統學習。實驗結果顯示，使用Smart 3D-UG的實驗組在幾何能力學習成就方面明顯優於對照組，並在學生學習幾何概念的過程中發現其中的錯誤概念，學生常因運算錯誤及粗心大意導致計算錯誤；又因幾何概念不清、公式混淆等導致錯誤的列式；又或是缺乏細心檢查而輸入錯誤，但因著GPT的智慧回饋，透過即時、針對性的指導，能幫助學生發現並修正錯誤，深化其對幾何概念的理解，以及適性化提供學生具體的建議與解題策略，從而增強其學習效率。
此外，本研究也針對合作學習進行學習行為與成就的分析，發現學生透過討論與合作共同解決問題，不僅提升學習成就，在學習動機、參與度及社交技能都有提升，亦幫助學生減輕學習壓力。實驗皆在真實情境中學習，將幾何概念融入生活中，使學生能以實際操作深化抽象概念的理解。因此，可知Smart 3D-UG系統搭配在真實情境使用，對學生學習體積與表面積有顯著的幫助。

摘要(英)

With the widespread adoption and use of smartphones, learning can now take place anytime and anywhere through a single device. Leveraging technology to support teaching has become a key goal in modern education, connecting technology with real-life environments and learning topics. This approach helps students learn in authentic contexts rather than confining learning to textbooks. Consequently, designing mobile-assisted learning programs has become more forward-looking, especially in addressing geometry-related scenarios in daily life. In response, a mobile application for geometry learning has been developed.
This study employs a mathematics and geometry learning system called Smart 3D-UG to help elementary school students learn about volume and surface area in real-life contexts. Smart 3D-UG incorporates augmented reality (AR) technology and intelligent feedback, enabling students to measure real 3D objects such as cubes, rectangular prisms, and triangular prisms. The system also includes a multimedia whiteboard for students to perform calculations directly.
In this study, 47 sixth-grade students were divided into an experimental group and a control group. The experimental group used Smart 3D-UG for learning, while the control group used the 3D-UG system without Smart features. The experimental results revealed that the experimental group significantly outperformed the control group in terms of geometry learning achievements. The study also uncovered common misconceptions students encounter when learning geometric concepts, such as calculation errors due to carelessness, confusion between formulas, and incorrect input due to a lack of careful checking. With the intelligent feedback provided by GPT, students received real-time, targeted guidance, helping them identify and correct mistakes, deepen their understanding of geometric concepts, and receive personalized suggestions and problem-solving strategies, thereby enhancing their learning efficiency.
Additionally, the study analyzed collaborative learning behaviors and achievements. It found that students improved not only their academic performance but also their learning motivation, engagement, and social skills through discussion and collaboration to solve problems. Collaborative learning also helped alleviate students′ learning pressure. Throughout the experiment, learning took place in real-life contexts, integrating geometric concepts into everyday life. This approach enabled students to use hands-on activities to deepen their understanding of abstract concepts, further strengthening their ability to apply knowledge. Therefore, it can be concluded that the Smart 3D-UG system, when used in authentic contexts, provides significant support for students in learning volume and surface area.

關鍵字(中)

★ 智慧機制
★ 真實情境
★ 幾何學習
★ 擴增實境
★ 合作學習

關鍵字(英)

★ Smart mechanism
★ uthentic context
★ geometry learning
★ augmented reality
★ collaborative learning

論文目次

摘要 I
Abstract II
致謝詞 IV
目錄 VI
圖目錄 X
表目錄 XII
第1章緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究問題 4
第2章文獻探討 5
2.1科技輔助教學 5
2.2在真實情境中的幾何學習 6
2.3幾何學習與錯誤概念 7
2.4合作學習於真實情境中的應用 8
第3章研究系統 9
3.1 系統介紹 9
3.1.1個人簡單與個人複合形體活動 11
3.1.2合作簡單與複合形體活動 14
3.1.3地圖 19
3.1.4白板 20
3.2 學習活動介紹 21
3.2.1學習材料 21
3.2.2學習歷程 21
3.2.3學習任務 22
3.3 智慧回饋 24
3.3.1學習歷程的智慧回饋 24
3.3.2計算的智慧回饋 25
3.3.3學生提問的智慧回饋 27
第4章研究方法 28
4.1 研究對象 28
4.2 研究架構 28
4.2.1自變項 29
4.2.2控制變項 30
4.2.3依變項 30
4.3 實驗流程 32
4.4 實驗設計 34
4.5 研究工具 35
4.5.1自編幾何能力測驗 35
4.5.2科技接受模型問卷 35
4.5.3訪談題目 36
4.6 資料蒐集與處理 36
4.6.1量化資料 36
4.6.2質性資料 36
第5章結果分析與討論 39
5.1幾何學習成就分析 39
5.2 學生於學習活動之學習行為分析 40
5.2.1學生任務作答情況 40
5.2.2學生數學幾何能力之錯誤概念 41
一、錯誤類型1：計算錯誤 42
(一)數學運算錯誤 42
1.進位和退位錯誤 42
2.括號使用錯誤 44
3.忽略運算優先次序 44
(二)粗心大意 45
二、錯誤類型2：公式錯誤 45
(一)幾何概念不清楚 45
(二)體積與表面積公式混淆 49
三、錯誤類型3：輸入錯誤 51
5.3 智慧回饋介入後學生錯誤概念改變情形及學習影響 52
5.3.1 GPT回饋後，學生個人任務答對率的變化情形 52
5.3.2 GPT回饋在表面積與體積的成效分析 53
5.3.3 GPT針對學生錯誤概念的回饋內容與分析 58
一、針對計算錯誤的GPT回饋與分析 58
(一)數學運算錯誤 58
1.進位和退位錯誤 58
2.括號使用錯誤 61
3.忽略優先次序 61
(二)粗心大意 62
二、針對公式錯誤的GPT回饋與分析 63
(一)幾何概念不清楚 63
(二)體積與表面積公式混淆 68
三、針對輸入錯誤的GPT回饋與分析 71
5.3.4智慧機制介入後學生的感知 74
一、智慧回饋功能對學生的感知 74
二、學習歷程功能對學生的感知 76
5.4合作學習對學生學習行為之影響 77
5.4.1個人學習與合作學習，學生答對率的變化情形 77
5.4.2合作學習優於個人學習的成效分析 78
5.4.3合作學習，學生學習行為與態度改變 80
一、提高學習動機 80
二、增強自信心 80
三、促進積極參與 81
四、改善社交技能 81
五、減少學習壓力 82
5.5真實情境下學習體積與表面積對學生的感知 83
一、增加學習的相關性和實用性 83
二、提高理解和記憶 83
三、增強問題解決能力與自主學習 84
四、增加學習動機和投入 84
5.6 科技接受模型（TAM）問卷分析 85
5.6.1 系統易用性 85
5.6.2 系統有用性 86
5.6.3 活動有用性 89
5.6.4 滿意度 91
5.6.5 系統使用意圖 92
第6章結論與建議 94
6.1 結論 94
6.2 限制與未來研究 96
參考文獻 97
附錄一前測試卷 102
附錄二後測試卷 106
附錄三科技接受模型問卷 110
附錄四訪談題目 116

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指導教授

黃武元(Wu-Yuin Hwang)

審核日期

2025-1-20

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